Comparison of dynamic behavior between continuous- and discrete-time models of intraguild predation

Ming Chen; Menglin Gong; Jimin Zhang; Lale Asik; Ming Chen; Menglin Gong; Jimin Zhang; Lale Asik

doi:10.3934/mbe.2023569

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 7: 12750-12771. doi: 10.3934/mbe.2023569

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Comparison of dynamic behavior between continuous- and discrete-time models of intraguild predation

1.
School of Science, Dalian Maritime University, Dalian 116026, Liaoning, China
2.
School of Mathematical Sciences, Heilongjiang University, Harbin 150080, China
3.
Department of Mathematics and Statistics, University of the Incarnate Word, TX 78209, USA

Academic Editor: Xiang-Sheng Wang

Received: 31 March 2023 Revised: 21 May 2023 Accepted: 22 May 2023 Published: 31 May 2023

Intraguild predation is a common ecological phenomenon that manifests itself by the aggression of one predator by another to obtain a shared prey species. In this paper, we develop a discrete analog of a stoichiometric continuous-time intraguild predation model. We analyze the dynamics of the discrete-time model, such as boundedness and invariance, stability of equilibria, and features of ecological matrices. The dynamic behavior of the two models is compared and analyzed through numerical analysis. We observe the same coexistence region of populations and stoichiometric effects of food quality of the shared prey in both models. Obvious differences between the discrete- and continuous-time models can be observed with intermediate and high levels of light intensity. The multistability characteristics and the existence interval of chaos differ among the different time scale models. This study provides evidence of the importance of time scales on intraguild predation.
- stoichiometry,
- discrete model,
- intraguild predation,
- food quality
Citation: Ming Chen, Menglin Gong, Jimin Zhang, Lale Asik. Comparison of dynamic behavior between continuous- and discrete-time models of intraguild predation[J]. Mathematical Biosciences and Engineering, 2023, 20(7): 12750-12771. doi: 10.3934/mbe.2023569

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Abstract

Intraguild predation is a common ecological phenomenon that manifests itself by the aggression of one predator by another to obtain a shared prey species. In this paper, we develop a discrete analog of a stoichiometric continuous-time intraguild predation model. We analyze the dynamics of the discrete-time model, such as boundedness and invariance, stability of equilibria, and features of ecological matrices. The dynamic behavior of the two models is compared and analyzed through numerical analysis. We observe the same coexistence region of populations and stoichiometric effects of food quality of the shared prey in both models. Obvious differences between the discrete- and continuous-time models can be observed with intermediate and high levels of light intensity. The multistability characteristics and the existence interval of chaos differ among the different time scale models. This study provides evidence of the importance of time scales on intraguild predation.

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